Basic properties
Modulus: | \(6012\) | |
Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1503}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.bb
\(\chi_{6012}(29,\cdot)\) \(\chi_{6012}(65,\cdot)\) \(\chi_{6012}(77,\cdot)\) \(\chi_{6012}(137,\cdot)\) \(\chi_{6012}(173,\cdot)\) \(\chi_{6012}(185,\cdot)\) \(\chi_{6012}(209,\cdot)\) \(\chi_{6012}(221,\cdot)\) \(\chi_{6012}(281,\cdot)\) \(\chi_{6012}(293,\cdot)\) \(\chi_{6012}(317,\cdot)\) \(\chi_{6012}(329,\cdot)\) \(\chi_{6012}(353,\cdot)\) \(\chi_{6012}(365,\cdot)\) \(\chi_{6012}(461,\cdot)\) \(\chi_{6012}(509,\cdot)\) \(\chi_{6012}(533,\cdot)\) \(\chi_{6012}(545,\cdot)\) \(\chi_{6012}(617,\cdot)\) \(\chi_{6012}(653,\cdot)\) \(\chi_{6012}(677,\cdot)\) \(\chi_{6012}(689,\cdot)\) \(\chi_{6012}(725,\cdot)\) \(\chi_{6012}(749,\cdot)\) \(\chi_{6012}(761,\cdot)\) \(\chi_{6012}(857,\cdot)\) \(\chi_{6012}(893,\cdot)\) \(\chi_{6012}(929,\cdot)\) \(\chi_{6012}(965,\cdot)\) \(\chi_{6012}(1013,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{73}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(77, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{498}\right)\) | \(e\left(\frac{29}{249}\right)\) | \(e\left(\frac{229}{498}\right)\) | \(e\left(\frac{64}{249}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{119}{498}\right)\) | \(e\left(\frac{23}{249}\right)\) | \(e\left(\frac{379}{498}\right)\) | \(e\left(\frac{205}{249}\right)\) |